# Correlation coefficient

# correlation coefficient definition

**Correlation coefficient** is a quantity that measures the strength of the **association** (or **dependence**) between two variables (x and y). For example if we are interested to know whether there is a **relationship** between the heights of fathers and son, a **correlation coefficient** can be calculated.

There are different correlation coefficients :

**Pearson r**: linear dependence**Kendall tau**: rank-based correlation coefficient**Spearman rho**: rank-base correlation coefficient

**Pearson correlation** is the most used one.

**correlation formula** is described here.

# Negative and positive correlation

The value of **correlation coefficient** can be **negative **or **positive** and it is comprised between **-1** and **1** (see the plots below).

**-1**means strong**negative correlation**: In this case y decreases when x increases (left panel figure)**0**means that there is no**relationship**between the two variables (x and y) (middle panel figure)**1**means strong**positive correlation**: In this case y increases when y increases (right panel figure)

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